After relaxation, we check that the structure has remained a covalently connected 2D material and not disintegrated into 1D or 0D clusters. This is done by defining clusters of atoms using the covalent radius[1]} + 30% as a measure for covalent bonds between atoms. The dimensionality of a cluster is obtained from the scaling of the number of atoms in a cluster upon repetition of the unit cell following the method described by Ashton et al. [2]}. Only materials containing exactly one cluster of dimensionality 2 are given further consideration (an exception is made for the metal-organic perovskites (prototype PbA\(_2\) I\(_4\) ) for which the metal atom inside the octahedron represents a 0D cluster embedded in a 2D cluster). To illustrate the effect of the covalent radius + 30% threshold, Figure REF  shows the distribution of the candidate structures in the database as a function of the covalent factor needed to fully connect the structure. Most materials have a critical covalent factor below 1.3 and fall in the green shaded region. There is, however, a tail of around 100 disconnected materials (red region); these materials are not included in the database.
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